JEE Math Practice Question
For $0<\theta<\pi / 2$, if the eccentricity of the hyperbola $x^2-y^2 \operatorname{cosec}^2 \theta=5$ is $\sqrt{7}$ times eccentricity of the ellipse $x^2 \operatorname{cosec}^2 \theta+y^2=5$, then the value of $\theta$ is :
- A.$\frac{\pi}{6}$
- B.$\frac{5 \pi}{12}$
- C.$\frac{\pi}{3}$
- D.$\frac{\pi}{4}$
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